It could be a couple of things. Either some type of fungal or bacterial decay is causing the colapse or the plant is expending the older flowers to put energy into the newer ones. If you are not sprinkler watering the plants so as to keep them wet the I doubt that the problem is due to disease.
It is difficult to diagnose the problem without seeing it, so I suggest that you take a sample from the plant along with a photo of the plant in its growing location (if possible) to your County Extension Office to see if they can help diagnose the problem and recommend an appropriate course of action.
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